A comparative study of the multi-objective optimization algorithms for coal-fired boilers

Combustion optimization has been proved to be an effective way to reduce the NOx emissions and unburned carbon in fly ash by carefully setting the operational parameters of boilers. However, there is a trade-off relationship between NOx emissions and the boiler economy, which could be expressed by Pareto solutions. The aim of this work is to achieve multi-objective optimization of the coal-fired boiler to obtain well distributed Pareto solutions. In this study, support vector regression (SVR) was employed to build NOx emissions and carbon burnout models. Thereafter, the improved Strength Pareto Evolutionary Algorithm (SPEA2), the new Multi-Objective Particle Swarm Optimizer (OMOPSO), the Archive-Based hYbrid Scatter Search method (AbYSS), and the cellular genetic algorithm for multi-objective optimization (MOCell) were used for this purpose. The results show that the hybrid algorithms by combining SVR can obtain well distributed Pareto solutions for multi-objective optimization of the boiler. Comparison of various algorithms shows MOCell overwhelms the others in terms of the quality of solutions and convergence rate.     

A multi-point sampling method based on kriging for global optimization

In general, sampling strategy plays a very important role in metamodel based design optimization, especially when computationally expensive simulations are involved in the optimization process. The research on new optimization methods with less sampling points and higher convergence speed receives great attention in recent years. In this paper, a multi-point sampling method based on kriging (MPSK) is proposed for improving the efficiency of global optimization. The sampling strategy of this method is based on a probabilistic distribution function converted from the expected improvement (EI) function. It can intelligently draw appropriate new samples in an area with certain probability according to corresponding EI values. Besides, three strategies are also proposed to speed up the sequential sampling process and the corresponding convergence criterions are put forward to stop the searching process reasonably. In order to validate the efficiency of this method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the higher global optimization efficiency of this method makes it particularly suitable for design optimization problems involving computationally expensive simulations.     

Incomplete sensitivities for 3D radial turbomachinery blade optimization

We are interested in optimal design of 3D complex geometries, such as radial turbomachines, in large control space. The calculation of the gradient of the cost function is a key point when a gradient based method is used. Finite difference method has a complexity proportional to the size of the control space and the adjoint method requires important extra coding. We propose to consider the incomplete sensitivities method for optimal design of radial turbomachinery blades. The central point of the paper is how to adapt some formulations in radial turbomachinery to the validity domain of incomplete sensitivities. Also, we discuss on how to improve the accuracy of incomplete sensitivities using reduced order models based on physical assumptions. Fine/Turbo flow solver is coupled with gradient based optimization algorithms based on CAD-connected frameworks. Newton methods together with incomplete expressions of gradients are used. The approach is validated through optimization of centrifugal pumps. Finally the results are considered and discussed.     

三种现代优化算法的比较研究

现代最优化算法比较常见的有遗传算法、蚁群算法、微粒群算法、人工鱼群算法等。本文主要对前三种算法优化性能进行比较研究。首先介绍了三种算法的基本原理,然后总结了各自的优缺点并从原理和参数两个方面对三种算法进行了对比分析,最后以经典TSP问题为例进行了仿真研究并得出了一些指导算法适用范围的结论。     

A comparative study of software systems from the optimization viewpoint

Analysis technology is widely accepted and quite popular these days. Incorporation of the analysis result into a design process is a key factor for the success of an analysis area. A few design software products have been commercialized. Generally, they are trying to make an interface between various design methods and analysis software. Optimization is a typical automatic design method. The software products of optimization are investigated and compared for user convenience and algorithm performance. A few popular products are selected. A graphical user interface (GUI) is compared for capability and efficiency. The performances of the optimization algorithms are tested by mathematical and engineering examples, and the results are discussed.     

A comparative study of multi-objective optimization algorithms for sparse signal reconstruction

The development of the efficient sparse signal recovery algorithm is one of the important problems of the compressive sensing theory. There exist many types of sparse signal recovery methods in compressive sensing theory. These algorithms are classified into several categories like convex optimization, non-convex optimization, and greedy methods. Lately, intelligent optimization techniques like multi-objective approaches have been used in compressed sensing. Firstly, in this paper, the basic principles of the compressive sensing theory are summarized. And then, brief information about multi-objective algorithms, local search methods, and knee point selection methods are given. Afterward, multi-objective sparse recovery methods in the literature are reviewed and investigated in accordance with their multi-objective optimization algorithm, the local search method, and the knee point selection method. Also in this study, examples of multi-objective sparse reconstruction methods are designed according to the existing studies. Finally, the designed algorithms are tested and compared by using various types of sparse reconstruction test problems.

     

Revolute manipulator workspace optimization: A comparative study

Robotic manipulators with three revolute families of positional configurations are very common in the industrial robots. The capability of a robot largely depends on the workspace of the manipulator apart from other parameters. In this work, an evolutionary optimization algorithm based on foraging behavior of Escherichia coli bacteria present in human intestine is utilized to optimize the workspace volume of a 3R manipulator. The proposed optimization method is subjected to some modifications for faster convergence than the original algorithm. Further, the method is also very useful in optimization problems in a highly constrained environment such as the robot workspace optimization. The test results are compared with standard results available using other optimization algorithms such as Differential Evolution, Genetic Algorithm and Particle Swarm Optimization. In addition, this work extends the application of the proposed algorithm to two different industrial robots. An important implication of this paper is that the present algorithm is found to be superior to other methods in terms of computational efficiency.     

A framework combining meshfree analysis and adaptive kriging for optimization of stiffened panels

Structural and Multidisciplinary Optimization - A framework is developed for structural optimization using an Element Free Galerkin (EFG) method for analyzing the structure, a kriging for surrogate...     

A comparative study on the metaheuristic-based optimization of skew composite laminates

Engineering with Computers - Plate structures are the integral parts of any maritime engineering platform. With the recent focus on composite structures, the need for optimizing their design and...     

A comparative study of optimization algorithms for low NOx combustion modification at a coal-fired utility boiler

NOx emissions from power plants pose terrible threat to the surrounding environment. The aim of this work is to achieve low NOx emissions form a coal-fired utility boiler by using combustion optimization. Support vector regression (SVR) was proposed in the first stage to model the relation between NOx emissions and operational parameters of the utility boiler. The grid search method, by comparing with GA, was preferably chosen as the approach for the selection of SVR’s parameters. A mass of NOx emissions data from the utility boiler was employed to build the SVR model. The predicted NOx emissions from SVR model were in good agreement with the measured. In the second stage, two variants of ant colony optimization (ACO) as well as genetic algorithm (GA) and particle swarm optimization (PSO) were employed to find the optimum operating parameters to reduce the NOx emissions. The results show that the hybrid algorithm by combining SVR and optimization algorithms with the exception of PSO can effectively reduce NOx emissions of the coal-fired utility boiler below the legislation requirement of China. Comparison among various algorithms shows the performance of the well-designed ACO outperforms those of classical GA and PSO in terms of the quality of solution and the convergence rate.     

A comparative study on optimization methods for experiments with ordered categorical data

When conducting experiments, the selected quality characteristic should as far as possible be a continuous variable and be easy to measure. Due to the inherent nature of the quality characteristic or the convenience of the measurement technique and cost-effectiveness, the data observed in many experiments are ordered categorical. To analyze ordered categorical data for optimizing factor settings, there are three widely accepted approaches: Taguchi’s accumulation analysis, Nair’s scoring scheme and Jeng’s weighted probability scoring scheme. In this paper, a simpler method named the weighted SN ratio method for analyzing ordered categorical data is introduced. A case study involving optimizing the polysilicon deposition process for minimizing surface defects and achieving the target thickness in a very large-scale integrated circuit can demonstrate the four approaches. Finally, comparative analyses of efficiency for employing the four approaches to optimize factor settings are presented according to simulated experimental data that are normally, Weibull and Gamma distributed. From the results, it is obvious that the weighted SN ratio method has the properties of easy computation and uses one-step optimization to obtain the optimal factor settings. Its efficiency is slightly less than that of the scoring scheme, better than that of the accumulation analysis and the weighted probability-scoring scheme.     

Update strategies for kriging models used in variable fidelity optimization

Many optimization methods for simulation-based design rely on the sequential use of metamodels to reduce the associated computational burden. In particular, kriging models are frequently used in variable fidelity optimization. Nevertheless, such methods may become computationally inefficient when solving problems with large numbers of design variables and/or sampled data points due to the expensive process of optimizing the kriging model parameters in each iteration. One solution to this problem would be to replace the kriging models with traditional Taylor series response surface models. Kriging models, however, were shown to provide good approximations of computer simulations that incorporate larger amounts of data, resulting in better global accuracy. In this paper, a metamodel update management scheme (MUMS) is proposed to reduce the cost of using kriging models sequentially by updating the kriging model parameters only when they produce a poor approximation. The scheme uses the trust region ratio (TR-MUMS), which is a ratio that compares the approximation to the true model. Two demonstration problems are used to evaluate the proposed method: an internal combustion engine sizing problem and a control-augmented structural design problem. The results indicate that the TR-MUMS approach is very effective; on the demonstration problems, it reduced the number of likelihood evaluations by three orders of magnitude compared to using a global optimizer to find the kriging parameters in every iteration. It was also found that in trust region-based method, the kriging model parameters need not be updated using a global optimizer—local methods perform just as well in terms of providing a good approximation without affecting the overall convergence rate, which, in turn, results in a faster execution time.     

Simulation physics-informed deep neural network by adaptive Adam optimization method to perform a comparative study of the system

Taking the marvelous advantages of artificial intelligence (AI) in accelerating the procedure of finding a solution to different engineering analyses is the main motivation of this article to establish a non-model-based mechanism on the basics of fully connected deep neural networks (FC-DNN) to analyze the hygro-thermomechanical buckling response of the multiscale hybrid composite MHC doubly curved panel. First, the system's buckling response at its design points is obtained by applying DQM to motion equations developed based upon the refined-form of third-order shear deformation theory (TSDT). Then the obtained information would be transferred to DNN to acquire the regressor system. Finding the optimal values of weights and biases of the DNN is the key factor to provide an AI system with high-accuracy prediction. For this reason, the adaptive Adam optimization approach is chosen due to its phenomenal speed as well as lower computational costs.

     

遗传算法在多目标优化应用中的对比研究

多目标优化应用研究在过程工程领域越来越受重视。本文首先给出了多目标优化问题的一般形式,指出多目标问题求解任务：引导搜索向整个的Pareto优化范围;Pareto优化前沿上保持解集的多样性。在简要论述遗传算法求解多目标技术的基础上,对应用了遗传算法求解多目标的两种方法进行了对比研究,并给出了线性加权遗传算法和一种多目标遗传算法的计算框图。指出线性加权法求解Pareto最优解时不能不能很好地处理非凸区域、均匀分布的权重值不能生成均匀分布的Pareto前沿等局限性,以及多目标遗传算法生成种群多样性及Pareto最优解均匀分布的优点,并用实例进行了验证说明。     

A comparative study on the performance of dissortative mating and immigrants-based strategies for evolutionary dynamic optimization

Traditional Genetic Algorithms (GAs) mating schemes select individuals for crossover independently of their genotypic or phenotypic similarities. In Nature, this behavior is known as random mating. However, non-random protocols, in which individuals mate according to their kinship or likeness, are more common in natural species. Previous studies indicate that when applied to GAs, dissortative mating - a type of non-random mating in which individuals are chosen according to their similarities - may improve their performance (on both speed and reliability). Dissortative mating maintains genetic diversity at a higher level during the run, a fact that is frequently observed as a possible cause of dissortative GAs’ ability to escape local optima. Dynamic optimization demands a special attention when designing and tuning a GA, since diversity plays an even more crucial role than it does when tackling static ones. This paper investigates the behavior of the Adaptive Dissortative Mating GA (ADMGA) in dynamic problems and compares it to GAs based on random immigrants. ADMGA selects parents according to their Hamming distance, via a self-adjustable threshold value. The method, by keeping population diversity during the run, provides an effective means to deal with dynamic problems. Tests conducted with dynamic trap functions and dynamic versions of Road Royal and knapsack problems indicate that ADMGA is able to outperform other GAs on a wide range of tests, being particularly effective when the frequency of changes is low. Specifically, ADMGA outperforms two state-of-the-art algorithms on many dynamic scenarios. In addition, and unlike preceding dissortative mating GAs and other evolutionary techniques for dynamic optimization, ADMGA self-regulates the intensity of the mating restrictions and does not increase the set of parameters in GAs, thus being easier to tune.     

A comparative study of stochastic optimization methods in electric motor design

The efficiency of universal electric motors that are widely used in home appliances can be improved by optimizing the geometry of the rotor and the stator. Expert designers traditionally approach this task by iteratively evaluating candidate designs and improving them according to their experience. However, the existence of reliable numerical simulators and powerful stochastic optimization techniques make it possible to automate the design procedure. We present a comparative study of six stochastic optimization algorithms in designing optimal rotor and stator geometries of a universal electric motor where the primary objective is to minimize the motor power losses. We compare three methods from the domain of evolutionary computation, generational evolutionary algorithm, steady-state evolutionary algorithm and differential evolution, two particle-based methods, particle-swarm optimization and electromagnetism-like algorithm, and a recently proposed multilevel ant stigmergy algorithm. By comparing their performance, the most efficient method for solving the problem is identified and an explanation of its success is offered.     

Global kriging surrogate modeling for general time-variant reliability-based design optimization problems

While design optimization under uncertainty has been widely studied in the last decades, time-variant reliability-based design optimization (t-RBDO) is still an ongoing research field. The sequential and mono-level approaches show a high numerical efficiency. However, this might be to the detriment of accuracy especially in case of nonlinear performance functions and non-unique time-variant most probable failure point (MPP). A better accuracy can be obtained with the coupled approach, but this is in general computationally prohibitive. This work proposes a new t-RBDO method that overcomes the aforementioned limitations. The main idea consists in performing the time-variant reliability analysis on global kriging models that approximate the time-dependent limit state functions. These surrogates are built in an artificial augmented reliability space and an efficient adaptive enrichment strategy is developed that allows calibrating the models simultaneously. The kriging models are consequently only refined in regions that may potentially be visited by the optimizer. It is also proposed to use the same surrogates to find the deterministic design point with no extra computational cost. Using this point to launch the t-RBDO guarantees a fast convergence of the optimization algorithm. The proposed method is demonstrated on problems involving nonlinear limit state functions and non-stationary stochastic processes.     

Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model

Coupled optimization methods based on multi-objective genetic algorithms and approximation models are widely used in engineering optimizations. In the present paper, a similar framework is proposed for the aerodynamic optimization of turbomachinery by coupling the well known multi-objective genetic algorithm—NSGA-II and back propagation neural network. The verification results of mathematical problems show that the coupled method with the origin NSGA-II cannot get the real Pareto front due to the prediction error of BPNN. A modified crowding distance is proposed in cooperation with a coarse-to-fine approaching strategy based on the iterations between NSGA-II and BPNN. The results of mathematical model problems show the effect of these improving strategies. An industrial application case is implemented on a transonic axial compressor. The optimization objectives are to maximize efficiencies of two working points and to minimize the variation of the choked mass flow. CFD simulation is employed to provide the performance evaluation of initial training samples for BPNN. The optimized results are compared with optimization results of a single objective optimization based on weighting function. The comparison shows that the present framework can provide not only better solutions than the single objective optimization, but also various alternative solutions. The increase of computational costs is acceptable especially when approximation models are used.     

A comparative study on reliability-index and target-performance-based probabilistic structural design optimization

Probabilistic structural design optimization enables designers and engineers to quantitatively take into account the uncertainties observed in the structural and environmental properties. In this paper, two approaches to determine the satisfaction of probabilistic constraints are discussed. One is the conventional reliability-index-based approach and the other is a more recently proposed target-performance-based approach. An algorithm, which detects and eliminates the excessive zigzagging iterations during the searches for the most probable failure point and the minimum performance target point, was incorporated.The number of iterations required by the two approaches was investigated in three examples: a cantilever beam, a three-bar truss and a ten-bar truss structure. Based on the results, the target-performance-based approach was found to be superior to the reliability-index-based one in view of both computational efficiency and numerical stability.     

A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations

This work is focused on the topology optimization related to harmonic responses for large-scale problems. A comparative study is made among mode displacement method (MDM), mode acceleration method (MAM) and full method (FM) to highlight their effectiveness. It is found that the MDM results in the unsatisfactory convergence due to the low accuracy of harmonic responses, while MAM and FM have a good accuracy and evidently favor the optimization convergence. Especially, the FM is of superiority in both accuracy and efficiency under the excitation at one specific frequency; MAM is preferable due to its balance between the computing efficiency and accuracy when multiple excitation frequencies are taken into account.